Overhead transmission lines are an essential component of power systems, being the most economical means of transmitting electricity from remote sources of generation to the customer. It is, therefore, vital that they be protected and maintained in service to ensure the security of the supply to the end-user, and to protect the capital investment of the power companies.Arcing faults are a common phenomenon on power systems and being able to understand the effects of fault arcs is important for power system protection. Numerical algorithms can be developed that locate the position of and analyse faults on power systems. The aim of this thesis is to develop accurate models of arcing faults and to develop numerical algorithms that can operate successfully on different power system topologies under various fault conditions.Comprehensive literature reviews have been completed the areas of electrical arcs and fault location algorithms. Existing arc models are investigated and new alternative methods of simulating them are proposed. A new method of modelling the elongation of secondary arcs is devised in this thesis and verified using real arc data. A new 'AirArc' model for use in fault simulations is proposed and its accuracy is verified by comparison with the behaviour of a real arc. Three new numerical algorithms, developed for this thesis, for fault location and analysis, based upon the synchronised sampling of voltage and current data at both ends of the line, are derived and their accuracy tested for a number of different network topologies and fault scenarios.Finally, there is a chapter summarising the work completed for this thesis, drawing conclusions from that work and suggesting further work that could be undertaken in the future.